examples of probable primes

To give an example of a probable primeMathworldPlanetmath relative to a base: 4341233-3341233 has passed preliminary primality tests relative to bases 2, 3, 5, 7, 11, 13 and 101. Its square root is approximately 2.336210102721, which makes a conclusive primality test by trial divisionMathworldPlanetmath in a reasonable time period impractical.

To give an example of a probable prime by a pattern: this pattern


suggests that 2170141183460469231731687303715884105727-1 might be a Mersenne primeMathworldPlanetmath. But since this is larger than the largest known Mersenne prime 230402457-1 (as of 2005), a Lucas-Lehmer test might take longer than the average human lifetime.

On the other hand, 12345678910123456789+123456789 is not a probable prime, because even though it is much larger than either of the probable primes given above, it is clearly divisible by 32.

Title examples of probable primes
Canonical name ExamplesOfProbablePrimes
Date of creation 2013-03-22 15:53:49
Last modified on 2013-03-22 15:53:49
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Example
Classification msc 11A41